Comparison of micro- and nano-size particle depositions in a human upper airway model

Aerosol Science 36 (2005) 211 – 233 www.elsevier.com/locate/jaerosci

Comparison of micro- and nano-size particle depositions in a human upper airway model Z. Zhanga , C. Kleinstreuera, b,∗ , J.F. Donohuec , C.S. Kimd a Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA b Department of Biomedical Engineering, North Carolina State University, Raleigh, NC 27695-7910, USA c Division of Pulmonary and Critical Care Medicine, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA d Human Studies Division, National Health and Environmental Effects Research Laboratory, U.S. EPA,

Research Triangle Park, NC 27711, USA Received 9 May 2004; received in revised form 10 August 2004; accepted 30 August 2004

Abstract Simulation results of microparticle and nanoparticle deposition patterns, local concentrations, and segmental averages are contrasted for a human upper airway model starting from the mouth to planar airway generation G3 under different inspiratory flow conditions. Specifically, using a commercial finite-volume software with usersupplied programs as a solver, the Euler–Euler (nanoparticles) or the Euler–Lagrange (microparticles) approach was employed with a low-Reynolds-number k–
model for laminar-to-turbulent airflow and submodels for particlephase randomization. The results show that depositions of both micro- and nano-size particles vary measurably in the human upper airways; however, the deposition distributions are much more uniform for nanoparticles. The maximum deposition enhancement factor, which is defined as the ratio of local to average deposition concentrations, ranges from about 40 to 2400 for microparticles and about 2 to 11 for nanoparticles with inspiratory flow rates in the range of 15
Qin
60 l/min. In addition, some airway bifurcations in generations G0 to G3 subjected to high inlet flow rates (say, Qin = 60 l/ min) may receive only very small amounts of large micro-size particles (say, with aerodynamic diameter dae  10
m) due to largely preferred upstream deposition. It has been hypothesized that, uniformly deposited nanoparticles of similar concentrations may have greater toxicity effects when compared to microparticles of the same material. 䉷 2004 Elsevier Ltd. All rights reserved. Keywords: Microparticle deposition; Nanoparticle deposition; Human upper airways; Computational fluid-particle dynamics

∗ Corresponding author. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh,

NC 27695-7910, USA. Tel.: +1 919 515 5216; fax: +1 919 515 7968. E-mail address: [email protected] (C. Kleinstreuer). 0021-8502/$ - see front matter 䉷 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jaerosci.2004.08.006

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1. Introduction The size of airborne particles or therapeutic aerosols determines not only how many particles may deposit, but also where these particles deposit in the respiratory system (Schulz, Brand, & Heyder, 2000). Size also influences the type of deposition mechanism. For example, particles with a mean diameter less than 0.5
m (i.e., nanoparticles), diffusional transport is dominant. For micro-size particles, inertial impaction is the main deposition mechanism in the upper (large) airways, and gravitational sedimentation governs their deposition in the small conducting airways and in the gas-exchange region of the lung. In general, the lung deposition fractions are small for particles in the size-range of 0.1
m
dp < 1
m. Besides the regional and total deposition fractions, local particle deposition patterns are another important parameter for health effect assessments of inhaled toxic or therapeutic aerosols (Schlesinger & Lippmann, 1978; Balásházy, Hofmann, & Heistracher, 2003). As indicated by Balásházy et al. (2003), local particle deposition patterns may play a key role in the development of lung cancer. It is very difficult and cost-intensive to determine local particle depositions by in vivo or in vitro tests, and hence, validated computational fluid-particle dynamics (CFPD) simulations can provide a noninvasive, accurate and cost-effective means to obtain such information for both particle-size groups. Considering a single bifurcation model which represents G3–G4 of Weibel’s lung model, Balásházy, Hofmann, and Heistracher (1999), Balásházy et al. (2003) quantified the inhomogenous local deposition patterns in terms of a deposition enhancement factor, which is defined as the ratio of local to average particle deposition concentrations. They attributed the apparent site selectivity of neoplastic lesion to the enhanced depositions of toxic particulate matter at bronchial airway bifurcations. However, in reality, the spacing between one or two successive bifurcations is insufficient for the flow to re-establish itself (Brucker & Schroder, 2003; Ramuzat & Riethmuller, 2002), i.e., particle transport and deposition vary significantly with bifurcations (Zhang, Kleinstreuer, & Kim, 2002a). Hence, multiple bifurcations, including upstream effects, need to be investigated. While ultrafine particles (i.e., dp < 100 nm) contribute very little in terms of mass fractions to ambient PM2.5 (or PM10), they may occur in substantial concentrations where nanomaterial is being manufactured (Dagani, 2003; Jortner & Rao, 2002). In any case, recent studies have found that many particles in the ultrafine size range are more toxic (i.e., they may cause more severe inflammation) than large, respirable particles made of the same material (Donaldson, Li, & MacNee, 1998; Frampton, 2001; Oberdörster, 2001; Oberdörster, Ferin, & Lehnert, 1994). For example, particles of titanium dioxide, aluminum oxide and carbon black of less than 50 nm in diameter have been shown to cause an approximately ten-fold increase in inflammation per unit mass than fine particles (Donaldson, Stone, Gilmour, Brown, & Macnee, 2000). These studies attributed the enhanced toxicity of nanoparticles to: (i) the greater surface area relative to the nanoparticle mass, and hence more sites to interact with cell membranes and a greater capacity to absorb and transport toxic substances such as acids (Chen, Miller, Amdur, & Gordon, 1992; Green et al., 1995; Gehr, Geiser, Im Hof, & Schürch, 2000); (ii) the prolonged retention time and the decreasing fraction of clearance for ultrafine particles (Scheuch, Stahlhofen, & Heyder, 1996); and (iii) possibly enhanced deposition of ultrafine particles in the deeper parts of the lung, including the alveolar region, where low surface tension produced by a surfactant film aids both nano- and micro-size particle transfer through the liquid wall layer (Gehr, Schurch, Berthiaume, Im Hof, & Geiser, 1990; Geiser, Schurch, Im Hof, & Gehr, 2000). However, the exact mechanisms of lung injuries by nanoparticles are still being explored. Hence, detailed comparisons between depositions of nanoparticles and microparticles in the

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213

human respiratory tract may provide more useful information for dosimetry-and-health-risk-assessments of differently sized particles. In this paper, considering a representative human upper airway model, the local deposition patterns as well as deposition efficiencies and fractions of particles in the nano-size range of 1 nm
dp
150 nm and in the micro-size range of 1
m
dae
10
m, where dae is the aerodynamic diameter, are simulated and compared. 2. Theory 2.1. Upper airway geometry As shown in Fig. 1, the present upper airway model consists of two parts: an oral airway model, including oral cavity, pharynx, larynx and trachea, and a symmetric, planar, triple-bifurcation lung airway model representing generations G0 (trachea) to G3 after Weibel (1963). The dimensions of the oral airway model were adapted from a human cast as reported by Cheng, Zhou, and Chen (1999). Specifically, the diameter variations along the present oral airway from mouth to trachea are almost the same as those for the hydraulic diameters from the cast. Variations to the actual cast only include the circular cross sections, a short mouth inlet with a diameter of 2 cm, a modified soft palate, and a strong bend. The dimensions of the four-generation airway model are similar to those given by Weibel (1963) for adults with a lung volume of 3500 ml. The airway conduits are assumed to be smooth and rigid. The minor effects of cartilaginous rings (Martonen, Yang, & Xue, 1994), which may appear especially in the upper airways, and out-ofplane bifurcations have not been considered in the present analysis. Although most bronchial bifurcations are somewhat asymmetric (Horsfield, Dart, Olson, Filley, & Cumming, 1971; Philips & Kaye, 1997) and non-planar, some studies (Chang, 1989; Liu, So, & Zhang, 2003) have shown that inspiratory flow in an asymmetric bifurcation exhibits the main features of the equivalent symmetric case. Non-planar geometries only influence the flow in downstream bifurcations (Caro, Schroter, Watkins, Sherwin, & Sauret, 2002; Zhang & Kleinstreuer, 2002). For inspiration, the air and particle flow fields in the nonplanar configuration resemble those in the planar configuration, but rotated to some degree and merged with the symmetric secondary vortices (Zhang & Kleinstreuer, 2002). While the non-planar geometry may somewhat increase microparticle deposition (Comer, Kleinstreuer, Hyun, & Kim, 2000), it has only a minor effect on nanoparticle deposition (Shi, Kleinstreuer, Zhang, & Kim, 2004). In summary, the present results, based on the symmetric branching geometries may be extrapolated to the asymmetric branching case with the corresponding local flow rate or non-planar geometries with corresponding rotations. 2.2. Governing equations Airflow. In order to capture the air flow structures in the laminar-to-turbulent flow regimes, i.e., 300 < Relocal < 104 for the present airway configuration and inhalation rates, the low-Reynolds-number (LRN) k–
model of Wilcox (1993) was selected and adapted. Zhang and Kleinstreuer (2003a) and Varghese and Frankel (2003) demonstrated that it is appropriate for such internal laminar-to-turbulent flows. All air flow equations, as well as initial and boundary conditions, including the adjustments of flow and particle information from the trachea of the oral airway model (see Section O-O in Fig. 1) as the inlet conditions of the bifurcating airway segment, are given in Zhang and Kleinstreuer (2003a,b). Transport of micro-size particles. With any given ambient concentration of non-interacting spherical microparticles, a Lagrangian frame of reference for the trajectory computations of the particles can be

214

Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233 Soft Palate

Mouth

Pharynx

Y

Glottis

Z

Larynx

X Trachea (G0)

O

O

Z

Trachea (G0)

Y B1 X

G1 G2 G3 B3.4

B2.2

B2.1 B3.1

B3.3

B3.2

Fig. 1. 3-D views of the oral airway model and bifurcation airway model (Generations G0–G3). B1—first bifurcation, B2.1 and B2.2—second bifurcation, B3.1, B3.2, B3.3 and B3.4—third bifurcation (the dashed lines indicate the segmental boundaries).

employed. In light of the large particle-to-air density ratio, dilute particle suspensions and negligible particle rotation, drag is the dominant point force. Hence, the particle trajectory equation can be written as (Zhang, Kleinstreuer, & Kim, 2002b) d 1 p p p (mp ui ) = dp2 CDp (ui − ui )|uj − uj |, 8 dt p

where ui and mp are the velocity and mass of the particle, respectively; CDp is the drag coefficient.

(1)

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215

In Eq. (1), ui is the instantaneous fluid velocity with ui = u¯ i + ui , where u¯ i is the time-averaged or bulk velocity of the fluid, and ui are its fluctuating components. Traditionally, turbulence is assumed to consist of a collection of randomly directed eddies; hence, an eddy-interaction model (EIM) is used to simulate the particle trajectories, and the fluctuating velocities ui are obtained by (Gosman & Ioannides, 1981; Matida, Nishino, & Torii, 2000; Schuen, Chen, & Faeth, 1983) ui = i ( 23 k)1/2 ,

(2)

where i are random numbers with zero-mean, variance of one, and Gaussian distribution. In the EIM, each particle is allowed to interact successively with various eddies and the random numbers are maintained constant during one eddy interaction, while the corresponding turbulence intensities vary with the particle positions (MacInnes & Bracco, 1992; Matida et al., 2000). The lifetime tE and length scale lE of the eddies which particles interact with can be determined as k 0.2 , tE = 1.51/2 C3/4 = 




and lE = C3/4

k 3/2 

= 0.164

k 1/2


.

(3)

Due to the assumption of turbulence isotropy, the fluctuating velocities normal to the wall calculated with Eq. (2) may be higher than the actual values (Kim, Moin, & Moser, 1987), which may overpredict the particle deposition in some cases (Matida, Finlay, Lange, & Grgic, 2002, 2004). As proposed by Matida et al. (2002, 2004), a near-wall correction can be used to simulate the near-wall particle trajectories, i.e., the component of fluctuating velocity normal to the wall un can be expressed as un = fv ( 23 k)1/2

(4)

with +

fv = 1 − e−0.02y ,

(5)

where fv is a damping function component normal to the wall considering the anisotropy of turbulence near the wall (Wang & James, 1999). Usually, Eq. (5) is used for y + < 10.0, while fv = 1 elsewhere. At the mouth inlet, presently uniform particle distributions were prescribed. The effect of randomized non-uniform particle inlet distributions on the deposition efficiency has been discussed by Zhang and Kleinstreuer (2001). The initial particle velocities were set equal to that of the fluid, and one-way coupling was assumed between the air and particle flow fields because the maximum mass loading ratio (mass of particles/mass of fluid) is below 10−4 in the present analysis. Particle positions and velocities in the cross section O-O (see Fig. 1) in the lower trachea were adjusted as the inlet particle conditions of the bifurcating airway segment. The regional deposition of microparticles in human airways can be quantified in terms of the deposition fraction (DF) or deposition efficiency (DE) in a specific region (e.g. oral airway, first, second and third bifurcation, etc.). They are defined as: DFparticle =

Number of deposited particles in a specific region , Number of partciles entering the mouth

(6)

DEparticle =

Number of deposited particles in a specific region . Number of partciles entering this region

(7)

The regional deposition efficiency is mainly used to develop the deposition equation for algebraic (total) lung modeling. The DEs and DFs are the same for the oral airway model in this study.

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Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233

The local deposition patterns of microparticles can be quantified in terms of a deposition enhancement factor (DEF). As proposed by Balásházy et al. (1999, 2003), the particle deposition enhancement factor is defined as the ratio of local to average deposition densities, where deposition densities are computed as the number of deposited particles in a surface area divided by the size of that surface area. The mathematical expression for DEF is DFi /Ai
n , i=1 DFi / i=1 Ai

DEF =
n

(8a)

where Ai is the area of local wall cell (i), n is the number of wall cells in a specific airway region, and DFi is the local deposition fraction in local wall cell (i) which is given as DFi =

Number of deposited particles in mesh cell (i) . Number of particles entering the mouth

(8b)

Clearly, if the overall and maximum DEF-values in one airway region are close to one, the distribution of deposited particles tends to be uniform. In contrast, the presence of high DEF-values indicates nonuniform deposition patterns, including “hot spots”. Some “hot spots” of toxic particulate matter are related to the induction of certain lung diseases (e.g., lung cancer). Mass transfer of nanoparticles. The convection-diffusion mass transfer equation of nanoparticles can be written as    *Y * * T *Y + D˜ + , (9) (uj Y ) = *t *xj *xj Y *xj where Y is the mass fraction, Y = 0.9 is the turbulence Prandtl number for Y , and D˜ is the effective aerosol diffusion coefficient which is calculated as follows (Cheng, Yamada, Yeh, & Swift, 1988; Finlay, 2001): D˜ = (kB T C slip )/(3dp ),

(10)

where kB is the Boltzmann constant (1.38×10−23 JK−1 ); and Cslip is the Cunningham slip correction factor. The regional deposition fraction can be determined according to Fick’s law (Zhang & Kleinstreuer, 2004), i.e.,     n   T *Y  DFregion = −Ai D˜ + (Qin Yin ), (11) Y *n i i=1

where Ai is the area of the local wall cell (i), and n is the number of wall cells in one certain airway region, e.g., oral airway, first airway bifurcation, etc. The local deposition patterns of nanoparticles can again be quantified in terms of a deposition enhancement factor (DEF) (see Balásházy et al., 1999, 2003), which is defined as the ratio of local to average deposition densities, i.e.,

  n     n      T *Y  T *Y  DEF = D˜ + (12) Ai D˜ + Ai . Y *n i Y *n i i=1

i=1

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217

Assuming that the airway wall is a perfect sink for aerosols upon touch, the boundary condition at the wall is Yw = 0. This assumption is reasonable for fast aerosol–wall reaction kinetics (Fan, Cheng, & Yeh, 1996) and also suitable for estimating conservatively the maximum deposition of particles or toxic vapors in airways.

3. Numerical methods The numerical solutions of airflow transport equations with low-Reynolds-number k–
model, were carried out with a user-enhanced commercial finite-volume based program, i.e., CFX4.4 from AEA Technology (2001), now ANSYS, Inc. The numerical program uses a structured, multiblock, body-fitted coordinate discretization scheme. In the present simulation, the PISO algorithm with under-relaxation was employed to solve the flow equations (Issa, 1986). All variables, including velocity components, pressure, and turbulence quantities, are located at the centroids of the control volumes. An improved Rhie–Chow interpolation method (AEA Technology, 2001) was employed to obtain the velocity components, pressure and turbulence variables on the control volume faces from those at the control volume centers. A Quadratic Upwind (QUICK) differencing scheme, which is third-order accurate in space, was used to model the advective terms of the transport equations. The sets of linearized and discretized equations for all variables were solved using the Block Stone’s method. The particle transport equation (Eq. (1)) was solved with an off-line F90 code with parallelized algorithms for the SGI Origin 2400 machine (Longest, Kleinstreuer, & Buchanan, 2004). For the calculation of particle trajectories, geometry, velocity and turbulence data at all control-volume vertices were first extracted from the CFX solution and written to arrays. A second-order improved Euler predictor-corrector method (Longest et al., 2004) was then used for the integration of the particle trajectory equation, including turbulent dispersion effects with near-wall correction (cf. Eqs. (2–5)). Particle deposition occurs when its center comes within a radius from the wall, i.e., local surface effects such as migration in mucus layers or resuspension due to clearing have been currently ignored. In the present simulations, 200,000 to 1,000,000 randomly selected, uniformly distributed particles were released at the mouth inlet. Particle deposition, including deposition efficiency and fraction, was tested to be independent of the number of particles released. The computational mesh was generated with CFX Build4, where the near-wall region requires a very dense mesh. Specifically, the thickness of the near-wall cells was chosen to fully contain the viscous sublayers and to resolve any geometric features present there. The mesh topology was determined by refining the mesh until grid independence of the solution of flow and mass fraction fields as well as particle deposition was achieved. The final mesh features about 420,000 and 670,000 cells for the oral airway and four-generation airway model, respectively. The computations were performed on an SGI Origin 2400 workstation with 32GB RAM and multiple 450 MHz CPUs. The solution of the flow field at each time step was assumed to be converged when the dimensionless mass residual, (total mass residual)/(mass flow rate) < 10−3 . The convergence of other variables was monitored as well. The estimated maximum artificial numerical dispersion coefficient is in the order of 10−11 m2 /s in this study, which is still one order smaller than the physical diffusion coefficient for the largest nanoparticle considered (3.2 × 10−10 m2 /s for 150 nm particles). Typical run times for the fluid flow and mass transfer simulations on eight processors with parallel algorithm were approximately 24–65 h for the oral

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Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233

airway model and 8 h for the four-generation model under steady inhalation condition. Utilizing the converged flow field solution, the microparticle trajectory simulations required approximately 10–25 h on four processors for each case simulated.

4. Model validations The present computational fluid-particle dynamics (CFPD) model has been validated with various experimental data sets for steady and transient laminar flows in bifurcations (Comer et al., 2000, 2001; Zhang & Kleinstreuer, 2002; Zhang et al., 2002b) and for laminar, transitional and turbulent flows in tubes with local obstructions (Kleinstreuer & Zhang, 2003; Zhang & Kleinstreuer, 2003a). Especially, the low-Reynolds-number (LRN) k-omega model has been extensively validated and has been proven to be an applicable approach to capture the velocity profiles and turbulence kinetic energy for laminartransitional-turbulent flows in the constricted tubes of the upper airways (see Zhang & Kleinstreuer, 2003a). The current simulation of nanoparticle deposition due to diffusional transport has been validated with both analytical solutions in straight pipes and experimental data for a double-bifurcation airway model (Shi et al., 2004) as well as experimental data in an oral airway model (Zhang & Kleinstreuer, 2003b). Simulated particle deposition fractions in the present oral airway model were compared with the observations by Cheng et al. (1999) in Fig. 2a for three inhalation rates. Following Cheng et al. (1999), the Stokes number is defined here as St = p dp2 U/9
D, with p being the particle density, dp being the particle diameter, and U being the mean velocity evaluated as (Q/A), where A is the mean crosssectional area, and D is the minimum hydraulic diameter. A comparison of microparticle deposition in the present airway model with in vivo deposition data as a function of the impaction parameter is shown in Fig. 2b. Generally speaking, our computational data points agree well with the experimental data and nicely retrace the mean of the measured deposition data curve. In summary, the good agreements between experimental observations and theoretical predictions instill confidence that the present computer simulation model is sufficiently accurate to analyze laminarto-turbulent fluid flow as well as mass transfer and particle deposition in three-dimensional oral and bifurcating airways.

5. Results and discussions The laminar-transitional-turbulent air flow and particle transport in the upper airway model under both steady and transient inhalation conditions have been previously analyzed (Kleinstreuer & Zhang, 2003; Zhang & Kleinstreuer, 2002, 2004). This paper will focus only on distinct features and underlying mechanisms of nanoparticle vs. microparticle depositions. 5.1. Microparticle deposition The 3-D surface views of the local particle deposition patterns in terms of particle deposition enhancement factor DEF (see Eq. (8a)) for particles with aerodynamic diameters dae = 3 and 10
m under different inspiratory flow conditions are shown in Fig. 3. Clearly, microparticle deposition during

Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233

Deposition Fraction (%)

100

219

Oral Airways

80 60 40 20 0 10-3

10-2 Stokes Number,

(a)

10-1

100

2 St=ρpdpU/(9µD)

Deposition Fraction (%)

100

80

60

40

20 0 101

(b)

102

103

Impaction Parameter,

104

2 daeQ (µm2 L

min-1)

Fig. 2. Comparison of the present simulated particle deposition fractions in the oral airway model with: (a) the experimental data of Cheng et al. (1999), (—) Correlation, (Cheng et al., 1999); ( ) Exper.data, (Qin = 15 l/ min, Cheng et al., 1999); () Exper.data, (Qin = 30 l/ min, Cheng et al., 1999); (♦) Exper.data, (Qin = 60 l/ min, Cheng et al., 1999); (䊉) Numer.Simulation, (Qin =15 l/ min); () Numer.Simulation, (Qin =30 l/ min); () Numer.Simulation, (Qin =601/ min); and (b) in vitro and in vivo deposition data sets, where dae is the aerodynamic particle diameter, (䊉) Number.Simulation data, (15
Qin
60 l/ min); ( ) (Cheng et al., 1999); () (Lippmann & Albert, 1969); () (Chan & Lippmann, 1980); (♦) (Foord, Black, & Walsh, 1978); (×) (Stahlhofen, Gebhart, & Heyder, 1980); (+) Stahlhofen et al. (1983); ( ) (Emmett, Aitken & Hannan, 1982); () (Bowes & Swift, 1989).

inhalation is mainly due to impaction, secondary flow convection, and turbulent dispersion. Thus, they mainly deposit at stagnation points for axial particle motion, such as the tongue portion in the oral cavity, the outer bend of the pharynx/larynx, and the regions just upstream of the glottis and the straight tracheal tube. As shown in Fig. 3, the maximum DEF-values are in the range of 43–479 for dae = 3 and 10
m, which vary with the flow rate. This implies that the deposition patterns of microparticles in the oral airway are highly non-uniform, and hence a small surface area, where the maximum DEF occurs, may receive hundred times higher dosages when compared to the average value for the whole airway. Such a site of

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Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233

Fig. 3. 3-D distributions of deposition enhancement factor (DEF) in the oral airway model for microparticles with: (a) Qin = 15 l/min; and (b) Qin = 60 l/min.

Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233

221

Fig. 4. 3-D distributions of deposition enhancement factor (DEF) in the airways G0–G3 for microparticles with: (a) Qin = 15 l/ min; and (b) Qin = 60 l/min.

massive particle deposition is usually located in the glottis region and/or at the outer bend in or just after the curved pharynx region. The contribution of turbulent dispersion on deposition seems to be stronger for small-size particles (say, dae = 3
m) than for larger-size particles (say, dae = 10
m) as indicated by more scattered and high DEF-values in the trachea. Figs. 4a and b depict the distributions of DEFs in the bifurcation airway model G0 to G3, i.e., part of the bronchial tree. As expected, for microparticles the high DEF values appear mainly around the carinal ridges due to inertial impaction, but the specific distribution of DEFs at each carina is different and varies with the inhalation flow rate as well. Some microparticles also land outside the vicinities of the carinal ridges due to secondary flows and turbulent dispersion. The strong turbulent fluctuations may occur just around the flow dividers and then decay rapidly in the straight tubular segments of the airways G0 to G3 (see Zhang & Kleinstreuer, 2004). It should be noted that no particles deposit in bifurcations B3.1 and B3.4 (see Fig. 1) in the case of Qin = 60 l/ min and dae = 10
m. In fact, no particles enter these two bifurcations because more than 80% of incoming particles deposit in the oral airways (i.e., for Qin = 60 l/ min and dp = 10
m). Figs. 5a and b show the maximum DEF-values in the oral airway model as a function of inspiratory flow rate and particle diameter as well as flow rate and Stokes number (St), evaluated at the trachea, i.e., St = (p dp2 U )/(18
D) with D being the diameter of the trachea (G0). In the oral airway model, the maximum DEF-values range from 40 to 550 for 15
Qin
60 l/ min and 1
dae
10
m, and their variations with flow rate and particle diameter are complex.A distinct peak of DEFmax can be found around St G0 ≈ 0.04 (i.e., Qin = 30 l/ min, dp = 7
m and Qin = 15 l/ min, dp = 10
m). Qualitatively, similar observations were reported by Balásházy et al. (2003) for microparticle deposition in a single-bifurcation

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Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233

Maximum Deposition Enhancement Factor

600 Oral Airway

Q in = 15 l/min

500

Q in = 30 l/min Q in = 60 l/min

400 300 200 100 0

2

4

6

8

10

12

Particle Diameter (µm)

(a) 600 Maximum Deposition Enhancement Factor

OralAirway

500 400 300 200 100 0 10-4

(b)

10-3

10-2

10-1

100

StG0

Fig. 5. Variations of the maximum deposition enhancement factor of microparticles in the oral airway model vs. flow rate and (a) particle diameter; and (b) Stokes number in the trachea.

model. With increasing Stokes number (particle size squared) the maximum number of particles deposited in a surface element may increase because of inertial impaction; however, the areas for receiving a high dose of deposited particles may also increase with Stokes number, which reduces the maximum DEFvalue (Balásházy et al., 2003). Also of interest is that the maximum DEF values for the high flow rate case (Qin = 60 l/ min) are lower than those for the low and medium flow rates. This is attributed to the strong turbulent dispersion and much broader distribution of deposited particles accompanied with the high airflow rate (see Fig. 3b). The variations of the maximum DEFs in the airways G0 to G3 with particle size and inspiratory flow rate or Stokes number (see Fig. 6a and b) differ from those in the oral airways. Generally, the maximum DEF-values range from 200 to 600 when St G0 < 0.01, but they increase rapidly with increasing St G0 when 0.01 < St G0 < 0.1. The highest DEF value can be about 2400, which is much greater than that in the oral airway model. This also indicates that highly variable microparticle deposition occurs in the tracheobronchial airways when compared to the oral airways. No distinct peak of DEFmax (dp , Qin = 30 l/ min) can be found in the bifurcating airways. This may be attributed to the upstream flow and deposition effects, which change the uniform particle distribution at the mouth inlet to a non-uniform distribution at the inlet of the bifurcating airways so that the deposited particles accumulate more closely in very small areas of the carinal ridges.

Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233

Maximum Deposition Enhancement Factor

3000 Qin= 15 l/min

2500

223

G0-3

Qin= 30 l/min Qin= 60 l/min

2000 1500 1000 500 0 2

(a)

4 6 8 10 Particle Diameter (µm)

Maximum Deposition Enhancement Factor

3000 2500 2000

G0-3

Qin= 30 l/min Qin= 60 l/min

1500 1000 500 0 10-4

(b)

Qin= 15 l/min

12

10-3

10-2

10-1

100

StG0

Fig. 6. Variations of the maximum deposition enhancement factor of microparticles in the airways G0–G3 vs. flow rate and (a) particle diameter; and (b) Stokes number in the trachea.

Considering the different local inlet Reynolds number, Stokes number, flow features and particle distributions at different individual bifurcations (i.e., B1, B2.1, B2.2, B3.1–B3.4), the distributions of DEFs as well as the maximum DEF-values change greatly at each individual bifurcation. Fig. 7 shows the maximum DEF-value variations vs. local inlet Stokes number for each individual bifurcation. The DEF for each individual bifurcation is calculated with Eq. (8a), where n is the number of surface elements in this bifurcation. It can be seen from Fig. 7 that the maximum DEF-values range mainly from 100 to 1000, which vary with airway bifurcation due to the different local flow characteristics and particle distributions when the local Reynolds and Stokes numbers are fixed. Fig. 8a and b present the variations of deposition efficiencies and fractions as a function of inlet Stokes number at each individual bifurcation. In the airway bifurcation B1, both the DE and DF increase with increasing Stokes number. However, the variation of DE(St), or DF(St), is irregular in airway bifurcations B2.1, B2.2 and B3.1–B3.4 because of the combined effects of flow developments and upstream deposition of particles entering from the mouth. Especially for relatively high Stokes numbers (say, St > 0.1), the strong aerosol deposition upstream (i.e., in the oral airway and first bifurcation) will greatly reduce both DEs and DFs in the second or third bifurcation. Thus, deposition data for large micro-size particles in the tracheobronchial airways are only accurate when the oral airways with reasonable inlet conditions are included.

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Maximum Deposition Enhancement Factor

103

102

101

First Bifurcation (B1) Second Bifurcation (B2.1, B2.2) Third Bifurcation (B3.1 -B3.4)

100 10-4

10-3 10-2 10-1 Stokes number at the parent tube

100

Fig. 7. Plots of the maximum deposition enhancement factor of microparticles for each individual bifurcation in the bifurcation airway model against local, inlet Stokes number.

Deposition Efficiency (%)

102

101

First Bifurcation Second Bifurcation Third Bifurcation

100

10-1

10-2 10-4

10-3

10-2

10-1

100

Stokes number at the parent tube

(a)

Deposition Fraction (%)

102

101

100

10-1

10-2 10-4 (b)

First Bifurcation Second Bifurcation Third Bifurcation

10-3 10-2 10-1 Stokes number at the parent tube

100

Fig. 8. Plots of (a) deposition efficiencies and (b) deposition fractions of microparticles for each individual bifurcation in the bifurcation airway model against local, inlet Stokes number.

Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233

225

Fig. 9. 3-D distributions of deposition enhancement factor (DEF) of nanoparticles in the oral airway model under steady inhalation with: (a) Qin = 15 l/ min; and (b) Qin = 60 l/ min.

5.2. Deposition of nanoparticles Again, the local deposition patterns of nanoparticles can be described in terms of DEF-distributions as given in Eq. (12). For a low inhalation flow rate (Qin =15 l/ min), the distributions of DEF (see Fig. 9a) in the trachea are measurably different with those for higher flow rate cases (Qin = 60 l/ min) (see Fig. 9b), because laminar flow still prevails after the throat contraction at Qin = 15 l/ min (Kleinstreuer & Zhang, 2003). Specifically, Fig. 9b shows the distribution of DEF for different size particles in the oral airway

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model with an inspiratory flow rate of Qin = 60 l/ min. For dp = 1 nm particles, the maximum enhanced deposition may occur at the entrance because of a great degree of mixing, i.e., a large concentration gradient in light of the assumed plug flow and uniform particle concentration at the inlet. The deposition decreases with the development of velocity and concentration fields in the oral cavity. With further complicated variations in flow and concentration fields in the pharynx, larynx and trachea, the deposition patterns are also inhomogeneous. The deposition of nanoparticles with 100 nm in diameter becomes more uniform, i.e., the maximum DEF decreases, when compared with those particles with dp = 1 nm and 10 nm. This is attributed to the significantly decreasing diffusivities and more uniformly distributed concentration fields in the tubes for larger nanoparticles (see Zhang & Kleinstreuer, 2004). In other words, as the particle size increases, wall depositions decrease and the air-particle mixtures become much more uniformly, featuring flat similar particle distribution profiles and hence wall gradients, which reduce the differences in local wall deposition rates. The location of maximum DEF may move from the mouth to the throat for 10 and 100 nm particles because of relatively homogenous and low deposition upstream and high near-wall gradients in particle concentrations in the areas of local tube constrictions. An increase in inhalation flow rate reduces the particle residence time and the chance for deposition. The decrease in wall deposition may cause more uniform concentration profiles in the conduits; as a result, deposition patterns do not vary as much for higher inhalation flow rates (see Qin = 60 l/ min in Fig. 9b) than for lower flow rates (cf. Qin = 30 l/ min and 15 l/min). Of interest is that the maximum DEF-values for nanoparticles are much lower than those for microparticles, i.e., the DEFmax for microparticles is of the order of 102 (see Fig. 3a and b), while DEFmax for nanoparticles is of the order of 1 (see Fig. 9a and b). As alluded to in the Introduction, a more uniform distribution of deposited ultrafine particles may relate to a greater toxicity effect when compared to fine particles made of the same materials. That is, not only the larger surface areas relative to the particle mass but also, more importantly, the larger surface areas with a near-uniform deposition can generate a higher probability of interaction with cell membranes and a greater capacity to absorb and transport toxic substances. Turning to the bifurcation airways G0 to G3, for example with an inspiratory flow rate of Qin =30 l/ min, Fig. 10 depicts the DEF-distributions for 1 nm
dp
100 nm. For both 1 nm and 10 nm particles, the enhanced deposition mainly occurs at the carinal ridges and the inside walls around the carinal ridges due to the complicated air flows and large particle concentration gradients in these regions. Specifically, the high concentration just upstream of the carina and zero concentration at the carinal ridge (i.e., generating high concentration gradients) lead to high diffusional depositions, as indicated by Eq. (11). This is consistent with the experimental observations of Cohen, Sussman, & Lippmann (1990). For 100 nm particles, the maximum DEF still occurs at the third carinal ridge; however, except at the entrance region, the DEF distribution tends to be more uniform due to the decrease in diffusion capacity. As a result, DEFmax for 100 nm particles is smaller than those for 1nm and 10 nm particles. Although the enhanced deposition sites (i.e., those with high DEF-values) in the bifurcating airways are similar for nano- and micro-size particles, the maximum DEF-values for nanoparticles are two to three orders of magnitude smaller than for microparticles. Fig. 11a and b show the maximum DEF-values as a function of particle diameter and inspiratory flow rate in the oral airway model and bronchial airway model, respectively. Clearly, DEFmax -values indicate “hot spots”, applicable to both toxic as well as therapeutic aerosols. In the oral airway, DEFmax may decrease with the decreasing inhalation flow rate since the deposition becomes more uniform at a higher flow rate with smaller residence times and mixing opportunities. In general, DEFmax also decreases with increasing particle size, but it may decrease more sharply for nanoparticles in the size range of 1–10 nm.

Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233

227

Fig. 10. 3-D distributions of deposition enhancement factor (DEF) of nanoparticles in the bifurcation airway model under steady inhalation with Qin = 30 l/ min.

DEFmax can approach asymptotic values of 2.2–3.0 when the particle diameter is larger than 50 nm and the inspiratory flow rate is in the range of 15
Qin
60 l/ min. The situation for DEFmax (dp ) in the bronchial airways becomes more complicated. When the particle diameter is smaller than 10 nm, the DEFmax does not exhibit a monotonic variation with flow rate. The DEFmax -values in generations G0–G3 vary little with particle size for very small nanoparticles and decrease sharply with particle size in the range of 10 nm to 30 nm. Again, the DEFmax can approach values around 2.4–3.0 when the particle diameter is larger than 100 nm and the inspiratory flow rate is in the range of 15
Qin
60 l/ min.

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Maximum Enhancement Factor

10 Oral Airway

8 6 4 Qin=7.5 l/min Qin=15 l/min Qin=30 l/min Qin=60 l/min

2 0 100

(a)

101 Particle Diameter (nm)

102

Maximum Enhancement Factor

12

8 6 Qin=7.5 l/min Qin=15 l/min Qin=30 l/min Qin=60 l/min

4 2 0

(b)

G0-3

10

100

101

102

Particle Diameter (nm)

Fig. 11. Variations of the maximum deposition enhancement factor of nanoparticles vs. flow rate and particle diameter in: (a) the oral airway model; and (b) the bifurcation airway model.

The variations of deposition fraction (DF) in the oral and G0–G3 airways vs. inhalation flow rate and particle diameter are depicted in Fig. 12. The DF is defined with Eq. (11) for nanoparticles and with Eq. (6) for microparticles. As expected, the variations of DF as a function of particle diameter are consistent with many previous experimental and theoretical studies. Specifically, with an increasing particle diameter the DFs decrease for nanoparticles because of the decrease in diffusive capacity while they may increase for microparticles due to increasing impaction. Similarly, the higher the inhalation flow rate, the lower the deposition of nanoparticles and the higher the deposition of microparticles. However, the inlet flow rate has a minor effect on nanoparticle deposition when compared to the influence of particle size. In fact, the deposition of 1 nm and 10
m particles in the oral airway may be as high as 20–40% and 10–80% while the DFs of 150 nm particles may be as low as 0.01–0.05%. The deposition fractions of very small ultrafine particles are comparable to those of large coarse particles in the upper human airways (see Fig. 12) as reported by Kim (2000). However, it should be noted that the local deposition enhancement factors for ultrafine particles are much lower than for coarse particles. Fig. 12b also shows that the DF in

Particle Deposition Fraction (%)

Z. Zhang et al. / Aerosol Science 36 (2005) 211 – 233 100 Oral Airway

90 80

Qin=15 l/min Qin=30 l/min Qin=60 l/min

70 60 50 40 30 20 10 0 10-3

Particle Deposition Fraction (%)

10-2

10-1

100

101

Particle Diameter (µm)

(a) 20 18 16 14 12 10 8 6 4 2 0

G0-3

Qin=15 l/min Qin=30 l/min Qin=60 l/min

10-3 (b)

229

10-2

10-1

100

101

Particle Diameter (µm)

Fig. 12. Variations of particle deposition fractions vs. flow rate and particle diameter in: (a) the oral airway model; and (b) the bifurcation airway model.

airways G0–G3 may not increase with the particle size for large microparticles (say, dae > 7
m) with a high inspiratory flow rate (Qin = 60 l/ min) because of the elevated deposition in the oral airway.

6. Conclusions The following conclusions can be drawn from the computational fluid-particle dynamics (CFPD) simulations: (1) The deposition patterns of microparticles in the upper airways are highly non-uniform. The maximum deposition enhancement factor (DEFmax ) ranges from 40 to 500 in the oral airway model and 200 to 2400 in the bronchial G0–G3 airway model for the parameter ranges 1
dae
10
m and 15
Qin
60 l/ min. Deposition efficiency, deposition fraction and deposition enhancement factor of microparticles in the tracheobronchial airways are dependent on the inlet flow rate and Stokes number

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(i.e., particle size squared) as well as the local geometry of the airway bifurcations. Some individual airway bifurcations (or generations) may receive only very small amounts of large micro-size particles due to strong upstream deposition. Hence, deposition data for large micro-size particles in the tracheobronchial airways are only accurate when the impact of the oral airways is included as well. (2) As with micro-size particles, deposition of nanoparticles occurs at greater concentrations around the carinal ridges when compared to the straight segments in the bronchial airways; however, deposition distributions are much more uniform along the airway branches. The deposition enhancement factors vary with bifurcation, particle size, and inhalation flow rate. Specifically, the local deposition is more uniformly distributed for relatively large-size nanoparticles (say, dp =O (100 nm)) than for small-size nanoparticles (say, dp =O (1 nm)). The maximum deposition enhancement factor in the upper airways can approach asymptotic values of 2.0–3.0 when the nanoparticle diameter is larger than 100 nm and the inspiratory flow rate is in the range of 15
Qin
60 l/ min. (3) The quite uniform distribution of deposited ultrafine particles also implies greater toxicity of ultrafine particles when compared to larger particles made of the same material. Hence, not only the greater surface area relative to the particle mass, but more importantly, the much broader deposition area can produce more sites to interact with cell membranes and a greater capacity to absorb and transport toxic substances. (4) Validated CFPD simulations of particle transport in the human airways can provide local and segmental particle depositions as a function of particle size, inhalation flow rate, and local system geometry. These results are invaluable for physical insight and the analyses of toxic/therapeutic aerosol deposition impacts in the lung. Disclaimer. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. EPA.

Acknowledgements This effort was sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF, under grant number F49620-01-1-0492 (Dr. Walt Kozumbo, Program Manager), the National Science Foundation (BES-0201271; Dr. Gil Devey, Program Director), and U.S. EPA (RTP, NC). The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The use of CFX software from ANSYS Inc. (Canonsburg, PA) and access to the SGI Origin 2400 workstation at the North Carolina Supercomputing Center (Research Triangle Park, NC), now defunct, are gratefully acknowledged as well.

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